Existence of Laplace Transform for Sin(t)/t

[Mizart]

I need to find out if the Laplace Transform of sin(t)/t exists without actually determining it.

Now, i do know a function needs to satisfy two conditions for its LT to exist which are 1. f(t) should be piece wise continuous and 2. f(t) should be of exponential order.

So my question is, how exactly do i verify if the function f(t) = sin(t)/t is of exponential order?

I have no idea how to do it theoretically so i tried doing it graphically. The graph of sin(t)/t expands infinitely towards the negative and positive x-axes which would mean its not of Exponential order, which in turn would mean it's LT doesn't exist. But im not entirely satisfied with this result.

So if anyone could tell me how do i determine the same theoretically or some formula which i might be missing out, i would really appreciate it.

Thanks!